BEYOND THE STANDARD MODEL

1. BEYOND THE STANDARD MODEL Dmitri Kazakov JINR/ITEP Outline Part I Supersymmetry Part II Extra Dimensions 1. What is SUSY 2. Basics of SUSY 3. The MSSM 4. Constrained MSSM 5. SUSY searches 6. SUSY DM 1. The main idea 2. Kaluza-Klein Approach 3. Brane-world models 4. Possible experimental signatures of ED

2. SU(3) The Standard Model SU(2) U(1) Forces Electromagnetic Particles Strong Weak H Gravity The Higgs boson

3. The SM and Beyond The problems of the SM: • Inconsistency at high energies due to Landau pole • Large number of free parameters • Formal unification of strong and electroweak interactions • Still unclear mechanism of EW symmetry breaking • CP-violation is not understood • Flavour mixing and the number of generations is arbitrary • The origin of the mass spectrum in unclear The way beyond the SM: • The SAME fields with NEW • interactions GUT, SUSY, String • NEW fields with NEW • interactions Compositeness, Technicolour, preons

4. Grand Unified Theories GUT • Unification of strong, weak and electromagnetic interactions within Grand Unified Theories is the new step in unification of all forces of Nature • Creation of a unified theory of everything based on string paradigm seems to be possible D=10

5. What is SUSY? • Supersymmetry is a boson-fermion symmetry • that is aimed to unify all forces in Nature including • gravity within a singe framework • Modern views on supersymmetry in particle physics • are based on string paradigm, though low energy • manifestations of SUSY can be found (?) at modern • colliders and in non-accelerator experiments First papers in 1971-1972 No evidence in particle physics yet

6. Motivation of SUSY in Particle Physics • Unification with Gravity • Unification of gauge couplings • Solution of the hierarchy problem • Dark matter in the Universe • Superstrings

7. Superalgebra Grassmannian parameters SUSY Generators This is the only possible graded Lie algebra that mixes integer and half-integer spins and changes statistics

8. Quantum States Quantum states: Vacuum = Energy helicity Total # of states:

9. SUSY Multiplets scalar spinor helicity -1/2 0 1/2 Chiral multiplet # of states 1 2 1 helicity Vector multiplet -1 -1/2 1/2 1 # of states 1 1 1 1 spinor vector Members of a supermultiplet are called superpartners For renormalizable theories (YM) spin For (super)gravity

10. Simplest (N=1) SUSY Multiplets Bosons and Fermions come in pairs Spin 0 Spin 1/2 Spin 1/2 Spin 1 Spin 3/2 Spin 2 scalar gravitino chiral fermion graviton vector majorana fermion

11. SUSY Transformation N=1 SUSY Chiral supermultiplet: parameter of SUSY transformation (spinor) spin=0 spin=1/2 Auxiliary field (unphysical d.o.f. needed to close SYSY algebra ) SUSY multiplets Superfiled in Superspace Expansion over grassmannian parameter superfield component fields

12. Gauge superfields Gauge superfield Field strength tensor Gauge transformation Wess-Zumino gauge Covariant derivatives physical fields

13. How to write SUSY Lagrangians 1st step Take your favorite Lagrangian written in terms of fields 2nd step Replace 3rd step Replace Grassmannian integration in superspace

14. Minimal Supersymmetric Standard Model (MSSM) SUSY: # of fermions = # of bosons N=1 SUSY: SM: 28 bosonic d.o.f. & 90 (96) fermionic d.o.f. There are no particles in the SM that can be superpartners SUSY associates known bosons with new fermions and known fermions with new bosons Even number of the Higgs doublets – min = 2 Cancellation of axial anomalies (in each generation) Higgsinos -1+1=0

15. Particle Content of the MSSM sleptons leptons squarks quarks higgsinos{ Higgses {

16. The MSSM Lagrangian The Yukawa Superpotential Superfields Yukawa couplings Higgs mixing term Violate: Lepton number Baryon number These terms are forbidden in the SM

17. R-parity B - Baryon Number L - Lepton Number S - Spin The Usual Particle : R = + 1 SUSY Particle : R = - 1 The consequences: • The superpartners are created in pairs • The lightest superparticle is stable • The lightest superparticle (LSP) should be neutral - the best candidate is neutralino (photino or higgsino) • It can survive from the Big Bang and form the Dark matter in the Universe

18. Interactions in the MSSM MSSM SM Vertices

19. Creation of Superpartners at colliders Annihilation channel Gluon fusion, ee, qq scattering and qg scattering channels

20. Decay of Superpartners squarks sleptons neutralino Final sates chargino gluino

21. Soft SUSY Breaking Hidden sector MSSM SUSY Messengers Gravitons, gauge, gauginos, etc Breaking via F and D terms in a hidden sector gauginos scalar fields Over 100 of free parameters !

22. MSSM Parameter Space • Three gauge couplings • Three (four) Yukawa matrices • The Higgs mixing parameter • Soft SUSY breaking terms mSUGRA Universality hypothesis (gravity is colour and flavour blind): Soft parameters are equal at Planck (GUT) scale Five universal soft parameters: in the SM versus and

23. Constrained MSSM Requirements: • Unification of the gauge couplings • Radiative EW Symmetry Breaking • Heavy quark and lepton masses • Rare decays (b -> sγ) • Anomalous magnetic moment of muon • LSP is neutral • Amount of the Dark Matter • Experimental limits from direct search Allowed region in the parameter space of the MSSM

24. Allowed regions after WMAP In allowed region one fulfills all the constraints simultaneously and has the suitable amount of the dark matter LSP charged WMAP Narrow allowed region enables one to predict the particle spectra and the main decay patterns Higgs EWSB Phenomenology essentially depends on the region of parameter space and has direct influence on the strategy of SUSY searches tan β =50

25. Mass Spectrum in CMSSM (Sample) SUSY Masses in GeV Fitted SUSY Parameters